System and method for imaging tendon cross sections for detecting voids and other deficiencies in grouted external tendons

ABSTRACT

An exemplary method of indicating a condition of grout within a post-tensioned tendon involves positioning a magnet and a metallic sensing plate in close proximity to an outer surface of the post-tensioned tendon; rotating the magnet and the metallic sensing plate around the outer surface of the post-tensioned tendon; measuring an amount of magnetic forces applied to the magnet during rotation of the magnet around the post-tensioned tendon; measuring an impedance between the metallic sensing plate and metallic strands within the post-tensioned tendon during rotation of the metallic sensing plate around the post-tensioned tendon; and generating an image of a cross-section of the post-tensioned tendon indicating one or more grout conditions in spatial proximity to the metallic strands within the post-tensioned tendon based on measurement data using the magnet and the metallic sensing plate.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a 371 U.S. National Phase entry of InternationalApplication No. PCT/US2020/041659, filed Jul. 10, 2020, which claims thebenefit of U.S. Provisional Patent Application No. 62/873,369, filedJul. 12, 2019, each of which are incorporated herein by reference intheir entirety for all purposes.

TECHNICAL FIELD

The present invention is generally related to assessing groutdeficiencies within building constructions.

BACKGROUND

Post-tensioned construction is a construction technique in whichportions of a structure, such as a bridge, are secured to each otherusing “tendons” that extend throughout the structure. The tendonscomprise an outer duct through which steel strands extend. Once thetendons have been placed into position, the strands are tensioned toprovide rigidity to the structure.

In order to prevent corrosion of the steel strands and improvemechanical performance, the ducts are filled with a grout material,which typically comprises a mixture of cement and water. When the groutis properly distributed within the duct, it creates a chemicalenvironment that protects the steel. When the grout is not properlydistributed, however, corrosion can occur. For example, if air gapsexist within the duct, the portions of the strands within those portionsare exposed and may corrode. Alternatively, if the grout is not mixedproperly or the mixture separates, regions that only contain water canbe formed, which also can lead to corrosion. Thus, harmful grout issuesor conditions in tendons include voids, spots of chalky grout, excessivewater content or even free water.

There is currently no economical and reliable method of nondestructivedetection of grout deficiency leading to corrosion within externalpost-tensioned tendon ducts. Corrosion can go undetected untilcatastrophic failure occurs potentially leading to structural failure,injury or loss of life.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the present disclosure can be better understood withreference to the following drawings. The components in the drawings arenot necessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the present disclosure. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1 is an exemplary embodiment of a tendon imaging unit in accordancewith various embodiments of the present disclosure.

FIGS. 2A-2B shows images of a physical prototype of an exemplaryembodiment of a tendon imaging unit in accordance with the presentdisclosure.

FIGS. 3A-3B show tendon specimen testing layouts for various groutconditions in accordance with the present disclosure.

FIG. 4 shows graphs depicting a modulus of impedance in kΩ versusangular position for the tendon specimen layouts of FIG. 3A for soundgrout conditions (top) and the grout condition involving water-filledvoids (bottom) in accordance with the present disclosure.

FIG. 5 shows images produced by an exemplary tendon imaging unit ofspecimens of FIGS. 3A-3B in accordance with various embodiments of thepresent disclosure.

SUMMARY

Aspects of the present disclosure are related to systems and methods forindicating a grout condition within a post-tensioned tendon. In oneaspect, among others, such a system comprises a force measuring sensorthat provides data indicating magnetic forces applied to a magnet and animpedance sensor that provides measurement data involving an impedancebetween a metallic sensing plate and metallic strands within thepost-tensioned tendon. In the system, a mechanism is adapted to mount tothe post-tensioned tendon and position the magnet and the metallicsensing plate in close proximity to an outer surface of the tendon, inwhich the mechanism is further adapted to facilitate moving of themagnet and the metallic sensing plate around the outer surface of thepost-tensioned tendon. Thus, a computing device is configured togenerate an image of a cross-section of the post-tensioned tendonindicating one or more grout conditions in spatial proximity to themetallic strands within the post-tensioned tendon based on at least dataprovided by the impedance sensor and the force measuring sensor.

Aspects of the present disclosure are also related to a method ofindicating a grout condition within a post-tensioned tendon. Such amethod comprises positioning a magnet and a metallic sensing plate inclose proximity to an outer surface of the post-tensioned tendon;rotating the magnet and the metallic sensing plate around the outersurface of the post-tensioned tendon; measuring an amount of magneticforces applied to the magnet during rotation of the magnet around thepost-tensioned tendon; measuring an impedance between the metallicsensing plate and metallic strands within the post-tensioned tendonduring rotation of the metallic sensing plate around the post-tensionedtendon; and generating an image of a cross-section of the post-tensionedtendon indicating one or more grout conditions in spatial proximity tothe metallic strands within the post-tensioned tendon based onmeasurement data using the magnet and the metallic sensing plate.

In one or more aspects, grout conditions are identified by a colormapping based on the data provided by the impedance sensor and/or theimage is generated by assigning a color-code to impedance measurementdata obtained from the metallic sensing plate. In one or more aspects, afirst color represents a normal grout condition, a second colorrepresents a full void grout condition, and a third color represents apartial void grout condition. In one or more aspects, a shading of thethird color represents a concentration level of water that is partiallyfilling a void in the grout.

In one or more aspects, an angular positioning module tracks positioningof the magnet and the metallic sensing plate as each travels around theouter surface of the post-tensioned tendon. In one or more aspects,positioning of the metallic strands is determined based upon force datasupplied by the force measuring sensor and/or a radial plot of thetendon is generated that identifies strand positions. In one or moreaspects, the image is generated by deconvoluting magnetic force valuesto generate a radial plot that provides an indication of a location ofthe strands within the tendon.

In one or more aspects, the force measuring sensor is a load cell, themechanism includes a shell member that mounts to the outer surface ofthe post-tensioned tendon, and/or the magnet and the metallic sensingplate are accommodated at opposite points of a circumference of theshell member.

Other systems, methods, features, and advantages of the presentdisclosure will be or become apparent to one with skill in the art uponexamination of the following drawings and detailed description. It isintended that all such additional systems, methods, features, andadvantages be included within this description.

DETAILED DESCRIPTION

The present disclosure describes embodiments of systems and methods forassessing grout deficiencies in building constructions using magneticand impedance sensing. In some embodiments, a magnet traverses thecircumference of the tendon and the force with which it is attracted tothe strands within the tendon is measured as a function of angularposition. Concurrently, an impedance sensor traverses the circumferenceof the tendon and measures an electric impedance between the impedancesensor and strands within the tendon. Variations in the electricimpedance between the sensor and the strands identify groutdeficiencies. The force and impedance information can then be used tocreate a radial plot that provides an indication of the location of thestrands within the tendon and an indication of grout deficiencies withinthe tendon.

Inadequate grouting has been found to be associated with a corrosion ofpost tensioning steel in grouted tendons used in bridges, as documentedin various notable cases over the last two decades. Groutingdeficiencies include voids where bleed water existed and was laterreabsorbed elsewhere or evaporated, regions of chalky low strengthgrout, and regions where excessive water content or even free water ispresent. In those zones, the mechanical bond between the steel strandand the grout is reduced and, of more concern, the strand steel riskscorrosion failure. Given these severe consequences, strict groutingquality guidelines are in place by specifying agencies requiring absenceof deficiencies, such as bleed water or voids, although seemingly notwidely addressing the degree to which those anomalies may become astatistical reality. Anomalies do develop to some degree and reliablenon-destructive testing (NDT) detection of grout anomalies is needed aspart of any approach to ensure long term integrity of post-tensioned(PT) bridges.

Nondestructive assessment of a grout condition is thus often needed,preferably by a cross section imaging method. However, such methods tendto be expensive to implement and slow to operate, as well as requirehealth risk management due to the use of penetrating radiation,resulting in limited deployment. Therefore, a non-destructive, rapid,inexpensive, and safe imaging method to detect grout deficiencies as anearly indicator of strand corrosion risk, and such is needed and is theobjective of the present disclosure.

In accordance with the present disclosure, a magnetic sensing approachto image the position of the steel strand bundle is combined with anelectric impedance approach to evaluate the condition of the groutspace. Both are embodied in a device that images the tendon's crosssection. The magnetic sensor has a magnet and a force measuringtransducer/sensor (e.g., load cell) and travels around the circumferenceof the tendon and measures the force of attraction between the magnet ofthe sensor and the steel strands, from which an image of the strandpattern inside the tendon is created. For example, the force attractiondata is converted into radial position information for the steel strandbundle, producing a base image of the tendon cross section, thusdelineating the location of the grout space. Simultaneously, a travelingimpedance sensor (e.g., a capacitance plate impedance sensor) rotatesaround the tendon and measures variations of the electric impedancebetween the impedance sensor and the strands in the tendon. Theimpedance variations identify a condition of the grout surrounding thestrands in the tendon, such as grout deficiencies. The impedance andstrand position data create a complete color-coded image of the tendoncross section indicating or flagging grout deficiencies. In addition tothe force and impedance data, an gyroscope/accelerometer device (e.g.,an angular positioning module) provides positional data on the sensorassembly, thus providing complementary positional data. Thus, measuredchanges in magnetic force and impedance values depending on strandposition can be acquired by the TIU. The overall information isintegrated by computation into a full image of the tendon cross section,mapping on near real time the extent and nature of the groutdeficiencies.

Such tools and techniques can serve as an important supplement toregularly scheduled bridge inspections like those under the U.S.Department of Transportation Federal Highway Administration (FHWA)National Bridge Inspection Standards, where for most bridges a routineinspection is required at 24 month intervals. Tendon cross sectionevaluations could be specified for locations selected on a spot schedulebasis in areas previously identified as high risk (e.g., near anchors,high points), but not formerly assessed. Alternatively, or as asupplement, this type of evaluation tool may be applied at unexpectedtendon failure events when urgent non-destructive testing imaginginformation of peer tendons not formerly assessed could help identifyother elements at risk. In all instances, the bridge owner receivesinformation on the presence and extent of grout deficiencies that canincrease the risk of corrosion of the tendon load bearing components.That knowledge, which may remain uncovered in the absence of a readilydeployable method such as presented here, can then be used for adjustingmaintenance strategies and their implementation from the standpoint ofbridge life cycle needs.

The electrical impedance of grout is a function of its dielectricproperties and the ionic conductivity of the pore solution, which areboth indicative of the grout condition. Various versions ofimpedance-related methods, in the form of electric capacitancetomography or of making the grout path as a part of an electronicoscillating circuit, have been proposed as well as deployed in actualpractice. However, while those applications identify grout anomaliesmanifested by changes in dielectric properties or conductivity,information on the spatial relationship between grout anomalies and thesteel strand bundle in the form of a cross-sectional visual image is atbest quite limited.

The combination of impedance with spatial image information is apowerful enhancement of tendon inspection tools and techniques. Forexample, interpretation of the significance of a detected groutdeficiency may vary depending on whether it is related to a small or toa large grout region in the cross-section space between the strandbundle and the duct wall. Moreover, the spatial information would alsoserve to refine the processing of the impedance values obtained, becausethe measured impedance depends not only on grout condition but also onthe thickness of the grout zone between the polymer duct wall and thesteel strand envelope.

Referring now to FIG. 1, an exemplary embodiment of a tendon imagingunit (TIU) 100 is presented. In one embodiment, a magnetic sensorassembly 110 and an impedance sensor assembly 120 are accommodated atopposite points of a circumference of a rotating shell 130, therebycreating an imaging unit that can slide along successive places on thetendon length. Accordingly, in various embodiments, a mechanismcomprising the shell member 130 can be temporality mounted to a tendon140 in a desired position along its length. As discussed, the tendon 140includes a duct 150 that surrounds multiple steel strands 160 and grout170. In the illustrated embodiment, the shell member 130 rotates aroundthe tendon 140.

In one embodiment, a magnet 115 is positioned in a center of an array offour ball-bearing rollers, keeping a nearly steady magnet face to outerduct surface distance of the tendon 140. The presence of theferromagnetic steel strands 160 in the tendon 140 can produce ameasurable attractive force on the magnet 115. By affixing the magnet115 to a load cell 118 (or other type of force measuring sensor)positioned so that the disk face of the magnet 115 is normal to theradius of the tendon cross section and by keeping the shell assembly 130at a fixed distance to the external surface of the tendon duct 150, theTIU 100 is configured to measure an amount of attractive force producedby the steel strands 160.

In one embodiment, a sensing plate 125 of the impedance sensor assembly120 is metallic and may be made of articulated stainless steel elasticsegments. The sensing plate 125 can be pressed closely against thesurface of the duct 150 by one or more springs in series. At anyselected place along the tendon 140, the combined action of a spring,flexible capacitive sensing plate 125 and bearings permitted smooth,hand actuated rotation of the TIU 100 while maintaining steadydimensional positioning of the sensors with respect to the tendonperimeter. Signal conditioning and initial processing can take place onan onboard electronic microcontroller 190, which includes a gyroscope“G” and an accelerometer “A” (that act as an angular positioning module)to keep track of angular position and data to adjust for gravitationaland centripetal forces. Further processing can be handled by executablesoftware at a computer 200 connected to the traveling combined TIU unit100. The resulting images from consecutive places provided a progressiveview of the tendon interior flagging grout anomalies.

For the magnetic module 110 and measurements, a disk-shaped permanentmagnet 115 (with magnetization normal to the disk face) placed near theexternal duct surface is operable to provide a magnetic field ofsufficient reach into the tendon 140. The presence of the ferromagneticsteel strands 160 in this field produces a measurable attractive forceon the magnet 115. The amount of attractive force is greater or smallerif the strand bundle surface was nearer or further respectively awayfrom the magnet 115. The force-distance behavior followswell-established relationships, so the force measurement can be readilyconverted into a radial distance value. Thus, the magnetic measurementstogether with the corresponding rotation angle values provided preciseinformation on the location of the strand bundle envelope within apolymer duct 150, creating an image of the bundle inside the duct 150.

In an exemplary embodiment, load cell data (involving the attractiveforces produced by the tendon strands 160) can be saved synchronous witha time array. The recorded force values are the result of convolution ofthe actual force values with the step function response of the magneticsensor 110—an effect not unlike motion blur in a photograph with apanning camera. To better approximate the actual force values, themeasured force data can be corrected by Fourier transform deconvolutionin a computer 200, using a separately measured determination of the stepresponse of the magnetic sensor assembly 110.

The electrical impedance (modulus), |Z|, measured by an impedance meteror monitor 128 of the TIU unit 100, is that of the capacitor formedbetween the metallic sensing plate 125 hugging the external surface ofthe tendon 140 and the metallic strand assembly inside the tendon 140.The strands 160 are all shorted together by the metallic anchor, whichin United States construction is usually connected to bridge ground. Thevarying impedance values provides an indication of the presence andextent of or absence of grout anomalies as a function of rotation angle.The impedance information (depending on grout condition) may then beused to color-code the space between the duct inner wall and the strandbundle in the image produced by the magnetic sensor assembly 110. Theresult is a near real-time cross section image of the tendon 140 on thedisplay of the processing computer 200, with grout deficienciesidentified by color mapping.

FIGS. 2A-2B shows images of a physical prototype of an exemplaryembodiment of the TIU 100. In particular, FIG. 2A provides an axial viewof an embodiment of TIU prototype and FIG. 2B shows a placement of theTIU prototype on a 114 mm diameter tendon. The TIU prototype features,but is not limited to only having, a clamshell-mounted unit body 130having a diameter of ˜180 mm and is ˜110 mm long. These compactdimensions and resulting small thickness on the tendon radius enabledimaging to extend to tight spots close to other tendons, structuralwalls, and anchoring or deviation block terminations. For thisparticular prototype design, a slender data cable reported measurementresults to a monitoring and display computer 200. An additional trailingcable connected the impedance circuit ground directly to bridge groundand hence to the strand bundle. From subsequent testing, it was foundalso that bridge ground may be practically replaced with a metal platewith enough capacitive coupling to the bridge segment floor, or evenmade unnecessary due to residual capacitive coupling to the surroundingstructure via the data cable and the computer 200.

For strand envelope sensing, the sensing magnet 115 of the TIU prototypewas tested and determined to have a magnetic moment of ˜4 A·m²,resulting in attractive forces to the ferromagnetic strand bundle near˜1N at the closest operating distances. In the prototype, the magnetrode in the center of an array of 4 ball-bearing rollers, keeping anearly steady magnet face to outer duct surface distance h of ˜2 mm. Theassembly was observed to tolerate cross section duct ellipticity (ratioof major to minor axes) as high as 1.1 while still maintainingsufficient magnet-duct clearance and providing useable force data.

The measured force data was corrected by Fourier transform deconvolutionin a host computer 200, using a separately measured determination of thestep response of the sensor. That response was treated in simplifiedform as an exponential settling with a characteristic time of ˜0.065seconds.

The corrected force information may then be processed to obtain valuesof the depth of the strand bundle envelope beneath the inner surface ofthe tendon duct 150, as a function of the angular position within thecross section. For simplicity, it was assumed that there is a power-lawdependenceF _(a) =k*z ^(1/n)  (Equation 1)between the corrected force F_(a), at a given angular position, and thelocal distance z at that angular position between the center of themagnet 115 and the edge of the strand envelope, with k as a constant andn as the exponent. It is noted that this treatment considers only thevalue of the force at a single angular position, so it is only anapproximate alternative to an otherwise computationally intensive fulldeconvolution operation. The results were nevertheless quite useful forthe intended purpose. To obtain optimized values of the parameters inEquation 1, the value of k was determined by experimental calibration;while for the more critical value of n (which tends to be large) finiteelement modeling calculations were performed with differentmagnet-strand combinations. Those calculations yielded values of k=207gF-cm^(n) and n=3.185 as a generic set with a provision for smallcalibration adjustments in specific TIU builds.

With the parameter values in place, the distance G from the inner ductperimeter to the strand envelope at a given angular position 6 wasobtained from the force value F_(a) there by

$\begin{matrix}{{G(\theta)} = {( \frac{k}{F_{a}(\theta)} )^{\frac{1}{n}} - ( {\frac{w}{2} + H + d_{D}} )}} & ( {{Equation}\mspace{14mu} 2} )\end{matrix}$where w is the magnet thickness, h is the distance between the magnetface and the external surface of the duct, do is the polymeric duct wallthickness, available from tendon construction data, or spot probing withminimal disruption at a representative location, or as an estimate(e.g., 6 mm) of typical values if precise imaging is not critical. TheG(θ) results were then presented in a polar plot format scaled to showthe outline of the strand envelope within a circular tendon crosssection in the form of a colored silhouette.

For impedance sensing, the assembled capacitive sensing plate 125 (of anexemplary impedance sensor assembly 120) measured 50 mm×50 mm square andwas pressed closely against the surface of the duct 150 by a combinationof the elastic interconnection of stainless steel elastic segments ofthe sensing plate 125 and one or more springs of the TIU assembly 100.This construction was robust and durable which allowed the plate 125 totightly fit during rotation against the duct eliminating intervening airspace. Despite that, the construction also minimized friction that wouldotherwise displace the plate 125 from its intended position, as well astolerated the minor duct surface scratches and similar irregularitiesnormally present in tendons in the field. Preliminary tests withlaboratory tendons evaluated the use of AC frequencies ranging from 0.1MHz to 10 MHz to measure the impedance behavior of various tendoncross-sections. Based on the results an operating frequency of 1 MHz waschosen, which provided a practical working compromise between adequatesensitivity to grout space property variations and simplicity ofimplementation.

For the present TIU assembly 100, the high frequency electrical behaviorof the system for a given angular position of the impedance sensorassembly 120 was abstracted as being that of a simple parallel-platecapacitor with a layered dielectric/conductive fill space. The curvatureand unevenness of the plate, tendon cross section, and strand bundlesurface were ignored, as were any non-uniform current distributioneffects. Also, by operating at a high enough frequency the impedances ofintervening interfaces were considered to be negligible so the measuredimpedance Z was here simplified asZ=Z _(D) +Z _(G)  (Equation 3)where Z_(D) and Z_(G) are the duct layer and grout space impedances,respectively.

As the duct material is normally quite uniform in composition andthickness (d_(D)), the impedance component Z_(D) was regarded as beingapproximately the same at all angles so variations in the measured valueof Z reflected mainly variations in Z_(G). Z_(G) depends on the localgrout space thickness d_(G) and on the grout composite condition. Thethickness dependence can be factored out if necessary, using theknowledge of the strand envelope position at each angle provided by themagnetic measurements. After accounting for thickness, variations in thevalue Z_(G) (and thus Z) serve as indicators of deficiency as shownnext.

The grout space is normally filled with sound hydrated grout, orotherwise by a composite mixture of some proportion of sound hydratedgrout and deficient space. The deficient portion include a void or voidsfilled with air or some water solution, unhydrated or partially hydratedgrout, or so-called soft or chalky grout with a high water to groutpowder ratio. Sound, deficiency-free grout behaves at a given testfrequency f as a material with an effective electric conductivity σ_(G)and dielectric constant ε_(G). Thus, the impedance of a notional groutspace with effective area A and depth d_(G) is inversely proportional tothe combination of those properties, as in a “leaky capacitor” analog:

$\begin{matrix}{Z_{G} = \frac{d_{G}}{A*( {{j*2*\pi*f*ɛ_{0}*ɛ_{G}} + \sigma_{G}} )}} & ( {{Equation}\mspace{14mu} 4} )\end{matrix}$where ε₀ is the permittivity of vacuum=8.85×10⁻¹² F·m⁻¹ and j=√{squareroot over (−1)}.

If the grout space incorporates deficiencies, it may still be viewed onfirst approximation as a uniform medium having effective values of σ_(G)and ε_(G), but different from those for sound grout. For a given groutpore structure both properties tend to increase in value with increasingwater content in the pores because of the greater degree of electricpore interconnection, as well as the high dielectric constant of watercausing a lower impedance value than that of sound grout. If the porestructure is more open due to a local excess of mixing water (a “soft”grout), the impedance decrease may be even more pronounced. A voidfilled with water, especially if it is highly conductive as in bleedwater, would represent an extremely low grout impedance case. If thedeficiencies consist instead of air-filled voids, it may be expectedthat as the fraction of affected space approaches unity (a “full void”),σ_(G) would tend to 0 and ε_(G) to 1, resulting in a markedly higherimpedance than that of sound grout. Correspondingly for deficienciesconsisting of unhydrated grout, those parameters would tend to beintermediate between the cases of full air voids and sound grout.Therefore, the value of Z_(G) and its variations can provide animportant indicator of the presence and extent of grout deficiencies.Per the form of Eq. 4, Z_(G) may be normalized by division by the valueof do thus focusing only on the deficiency-sensitive property changes.As it will be shown, changes in grout properties alone were in manycases dominant, so for practical implementation grout space thicknessnormalization was not built in the data processing algorithms. Thatchoice was not limiting, however, and it can be readily implemented invarious embodiments.

For simplicity of operation and given that Z_(D) is nearly 267 constant,variations in the value of the total impedance Z (rather than of Z_(G)which would have required additional processing) were used as the mainindicator of deficiencies. Impedance values are complex numbers with areactive (imaginary) and a resistive (real) part, and separateevaluation of those components has the potential of being more revealingof the nature and extent of the deficiencies. However, preciseseparation is instrumentally demanding and previous tests have shownthat grout anomalies were sufficiently revealed by changes in themodulus of the impedance, here designated as |Z|. That value, which isequal to the quadratic combination of both parts, is less costly toimplement instrumentally with the necessary accuracy and it was adoptedas the detection parameter for the TIU 100. Thus, the impedance sensorassembly 120 produced a time-synchronized |Z|(θ) data stream that wassent to a processing unit or computer simultaneous with the force loaddata from the magnetic sensor assembly 110.

In accordance with various embodiments of the present disclosure, theimpedance indication of grout condition together with the strandposition information, may then be combined into a color-coded 2D imageof the cross section indicating or flagging grout deficiencies andspatial context. For operation, rotating the ring one full turn aroundthe tendon 140 produced simultaneous 360° angular profiles of themagnetic force and impedance modulus, which were registered tocorrespond to the values for coincident angular positions and stored ina data file on the monitoring and display computer 200. Impedance andangular position data acquisition rate was 10 Hz. From there the datawas filtered, conditioned, and processed in order to generate thecross-sectional image of the tendon 140. Typically, a full rotation scanand associated image display was completed in only 10 seconds. Theprocedure yielded a set of less than 100 data points that were properlyparsed based on the gyroscope readings, so that the displayed patternwas nearly insensitive to variations in rotation speed that may havetaken place during the image acquisition. Furthermore, a calibrationprocedure was developed for field applications as discussed later on.

Notably, the entire unit and housing of the TIU prototype (FIGS. 2A-2B)was made with readily available components and ordinary 3D printingequipment. Thus, the TIU prototype can be quickly and inexpensivelyreplicated if multiple units need to be deployed at a field site foreither routine or emergency assessment. Such deployment is furtherfacilitated by simplicity of operation that does not require specializedpersonnel, has compact dimensions, and a fast display of results.

A first set of experiments, used for development of a magnetic strandlocation method, was conducted with the central region of five legacytendon segments from a prior investigation. The ˜0.30 m tendon segmentshad an 89 mm external diameter high-density polyethylene (HDPE) of 5.5mm wall thickness. The tendons had twelve ASTM A416 12.7 mm nominaldiameter size, 7-wire formerly stressed steel strands fully embedded inQPL-938 Masterflow® 1341 grout which had no significant magneticsusceptibility. During construction, the strands were evenly distributedat the anchor ends, but placement within the cross section of the tendonsegments tested varied from even to strongly lopsided depending on theirproximity to a deviation block bend. An early developmental magneticimaging-only version of the TIU prototype was used for those tests.

The main laboratory evaluation of the combined magnetic-impedanceimaging approach was conducted with tendon segment specimens rangingfrom 89 mm to 114 mm nominal diameters. FIGS. 3A-3B shows the specimenlayouts for four specimens labeled #1A, #1B, #2, and #3. Each of the#1A, #1B, and #2 specimens shared longitudinal dimensions and centralvoid position. Depth dimension d for a central void measures 30 mm, 35mm, and ˜13 mm for #1A/#1B, #2, and #3 respectively. Plate anglereference and orientation, illustrated for #2, was common in all tests.

The smaller diameter specimens (#1A and #1B in FIG. 3A) with a ˜5.6 mmHDPE thickness were a set of two replicates, each ˜0.76 m long, thatcontained twelve unstressed ASTM A416 12.7 mm nominal diameter size,7-wire steel strands lumped away from the center with a 102 mm longcentral void with a volume of ˜215,000 mm³.

One of the 114 mm diameter specimens (#2 in FIG. 3B), with a ˜7 mm HDPEthickness, was a ˜0.76 m long laboratory sample that contained nineteen12.7 mm steel strands lumped away from the center with a 102 mm longvoid similar to that in the smaller diameter tendons, with a volume of˜300 mL.

The other 114 mm diameter specimen (#3 in FIG. 3B) was extracted fromthe John Ringling Causeway Bridge, that had experienced strand corrosionincidents. The segment was 1.55 m long with twenty-four 12.7 mm strandsand a HDPE thickness of ˜7 mm. The segment had no recognizable nativegrout deficiencies, so a ˜100 mm long grout void, centered ˜300 mm fromone end, was chiseled in the lab. That void had a volume of ˜80 mLreaching from the inner surface of the duct 150 to the strand envelope.

The voids in the laboratory tendons were created by placing apolystyrene foam insert of the desired approximate dimensions in themold before casting the grout. After curing, the foam was dissolved byinserting a small amount of acetone via a small hole in the duct wall.The acetone then evaporated leaving a solid residue with volume only ˜1%of that of the initial insert, and a full void of nearly the same sizeas the insert. The duct wall hole, re-sealable with a polymeric plug,allowed for temporary insertion and removal of alternative void fillingsthat included unhydrated grout and water (for the smaller diametertendons), without substantially affecting the condition of the rest ofthe tendon segment. For the bridge tendon segment, the grout was firstexposed by cutting out a ˜70 mm by ˜100 mm rectangle of the duct 150,which was afterwards reattached at the edges with an epoxy compound,leaving a smooth external surface over and around the void. Theapproximately greatest depth of each void, d, is shown in FIGS. 3A-3B aswell.

Specimens (#1A, #1B, and #2) were cast with the EUCO Cable Grout PTXproduct, with a water to grout ratio of 0.23, as recommended permanufacture's specifications (EUCO 2017). This material had noticeablymagnetic susceptibility, with effects discussed later on. Evaluationswere conducted at curing ages ranging from ˜5 months to ˜2 years. Thehydrated grout had a density of ˜2.0 g/cm3, and resistivity in the orderof 100,000 ohm-cm at the age ˜193 days of the imaging evaluations.Angular coordinates used are shown in FIGS. 3A-3B. For a point in theinner wall of the duct 150, the voids spanned an angular range ofsomewhat <˜180° for the laboratory tendons, and <˜90° for the fieldtendon. All tests were conducted using the TIU prototype of FIGS. 2A-2B,at laboratory ambient temperature (˜22° C.), and included the followingconditions and testing setups.

To evaluate a sound/normal grout condition, the rotating TIU unit 100was centered on an axial position on the tendons 140 halfway between theedge of the central void and the end of the tendon. Thus, the magneticand impedance sensors were centered on a sound grout region ˜1.5 tendonduct diameters clear from any variation. For the field tendon, the TIUunit 100 was centered on tendon axis point ˜300 m away from the edge ofthe void region, with a clear sound region >3 tendon duct diameters.

For a grout condition having an air-filled void (as indicated in FIGS.3A-3B), image acquisition was performed with the TIU unit 100 positionedon the center of each of the pictured voids and for all specimens. For agrout condition having a filled void space, the void space was filledwith unhydrated dry grout powder, simulating an unmixed grout plugextreme condition sent into the tendon. The unhydrated powder had adensity of 1.2 g/cm³. This condition was examined with the #1A and #1Breplicate specimens, in which the powder was removed from the void aftercompletion of testing. For a grout condition having a void filled withdiluted water, the void space was filled with a mildly alkaline watersolution with pH (as determined with pH color-indicating paper) rangingfrom 8 to 10 depending on prior condition of the void space. Thissolution was created by inserting deionized water in the cavity andallowing interaction for ˜15 minutes with the grout at the cavity wallsor residual unhydrated grout particles from a previous test condition.The condition explored the ability of detecting the outcome of anextreme water segregation event during grout preparation, which wouldhave resulted in only minor ionic species presence. This condition wasexamined with the #1A and #1B replicate specimens and testing wasconducted 15 minutes after introduction of water into the void, afterwhich the water was drained from the void after completion of testing.For a grout condition having a void filled with concentrated water, thevoid space was filled with a highly alkaline NaOH water solution(pH˜13.5, ˜0.3M NaOH, resistivity ˜20 Ω-cm). This solution is asimplified analog of the pore water often encountered in cementitioussystems, where K and Na cations create a highly alkaline mixture withhigh electric conductivity. The condition may resemble a void filledwith bleed water or similar high ionic content liquid segregation thattook the place of otherwise sound grout. Examined only with the #1A and#1B replicate specimens; tests conducted 15 minutes after introductionof solution into the void, after which the solution was drained away.This condition was evaluated after the Dilute Water tests.

To ensure that no air gap remained in the cavity when a condition wasbeing introduced certain precautions were taken. For the unhydrated (UH)grout condition, the powder was compacted, and the tendon specimen wasvibrated and tapped with a mallet. For the water conditions, thespecimens were only vibrated and tapped, and the cavity was allowed tooverflow and then dried with a towel paper to make sure the polymer ductwas dry.

Overall trends of impedance measurements and reproducibility areillustrated in FIG. 4 for the results from replicate specimens #1A (onleft side of figure) and #1B (on the right side of figure). There, theimpedance modulus |Z| is shown as a function of angular position of thesensing plate center with 180° corresponding to the apex where thethickest grout space, or alternatively the highest void space is locatedper FIGS. 3A-3B. Trends were generally the same in the replicatespecimens, attesting to reproducibility of the technique and findings.Variation in one case (Dilute Water) was ascribed to test sequencingdifferences. Additional tests, not shown in the figures, consisted ofimmediately consecutive measurements for each condition and specimen(including as well specimens #2 and #3) so as to assess repeatability.It was evaluated as the root mean square relative difference (inpercent) between the impedances measured in the consecutive tests,computed at regular interpolated intervals over 360°. Results rangedfrom 0.28% to 5.35%, with 1.68% on average. Those indications of datastability were deemed sufficient for useful application of the tendonimaging method in the conditions evaluated here.

For the sound grout condition, the impedance modulus |Z| varied modestlyaround the duct perimeter, with only a faint maximum near 180°. This isas expected since the dominant impedance is that of the duct wall, whichis nearly constant around the tendon. |Z| for the wall is ofsignificantly higher value (in the order of 10 kΩ for the frequency,duct wall thickness, HDPE dielectric constant, and plate dimensionsused) than that of the sound grout space (about 1 order of magnitudesmaller). The combination of those estimated values is also in goodagreement with the experimental observation. The maximum is more visiblein the magnified plots shown in the lower part of FIG. 4 and reflectsthe grout space at 180° being about 3 times greater than near 0°, due tothe crowding of the strands 160 near the bottom.

Much stronger detection differentiation was obtained for the Voidcondition. In both specimens, there was a pronounced maximum in |Z| near180°, to about two to three times the value at the opposite end of theperimeter (˜0°) where only sound grout is present. The value of |Z| at0° was nearly the same as for the sound condition when it existed overthe entire perimeter. The impedance maximum was moderately shifted inboth specimens from an ideal 180° angle. This behavior, confirmed inrepeat tests, likely reflected some degree of specimen constructiondeviation on void forming and casting.

The Unhydrated Grout condition resulted also in a strong differentiationfrom the Sound case, with a marked maximum near 180°, about ⅔ of themagnitude observed with the full Void condition. The high impedance ofthe unhydrated grout with respect to that of the sound, hydrated groutwas to be expected on various considerations. The amount of cementitiousmass per unit volume is expected to be significantly less than that ofhydrated grout due to the granular structure without fluid accommodationassistance, so any dielectric behavior inherent to the cementitiouscomponents should be correspondingly reduced. Importantly, the highdielectric contribution from the presence of water is absent inunhydrated grout, and electrolytic conductivity is also absent withoutthe presence of water. Thus, the impedance of unhydrated grout should bethat of a non-conducting granular material with effective averagedielectric constant only modestly higher than that of air. The overalleffect was impedance modulus values in between those of sound grout anda full void, somewhat closer to the latter, and in any event clearlydetectable.

The Concentrated Water (CW) fill condition yielded impedance values near180° that were moderately but consistently lower than those of soundgrout in the same region, as shown in the enlarged bottom graphs of FIG.4. This differentiation reflected the high dielectric constant of water(near 80 compared to a value ˜ one order of magnitude lower for soundgrout), combined with strong ionic conductivity from the ˜0.3 Mdissolved NaOH. Those factors markedly lowered the impedance of thefilled space compared to that of sound grout, resulting in the dipmeasured near 180°. It is noted that the water closely filled the entirevoid space, leaving no significant gap near the inner duct surface andtherefore allowing for the presence of the highlypermittivity/conductive medium to be manifested in the measuredimpedance changes. The overall relative effect, however, is limited,because of the constant presence of the duct wall and its high seriesimpedance component. Consequently, unlike the cases of the void (V) orunhydrated (UH) grout, the change is only in the order of 10% to 20% ofthe sound grout case total impedance, so sensitivity to the presence ofthe simulated bleed water is accordingly only moderate. The impedanceresponse for the lower, normal grout portion of the specimen was, asexpected and as in the other cases, much closer to that encountered forthe same region in the Sound condition.

The response to the Dilute Water (DW) condition was in one of thereplicate test specimens (#1A) quite close to that for the concentratedwater, while for #1B it was somewhere intermediate between the Sound andthe Concentrated Water conditions. This behavior is consistent with thecircumstance that #1A was tested immediately after completing theunhydrated grout tests. Interaction with residual grout particleselevated the solution pH (to˜10), evidencing ionic enrichment andcorresponding decrease in solution resistivity and lower impedance ofthe intervening space. In contrast, water introduction in specimen #1Btook place at a time when the inner space had experienced priorflushing, resulting in only a mildly alkaline solution (pH ˜8). Thus,only the impedance decrease associated with the high dielectric constantof water appears to have been of importance. That dielectric effectalthough diminished was still evident when contrasted with the Soundgrout condition, so the impedance measurements showed reasonablepotential for detection of a free water condition even when ioniccontent was minor.

Specimens #2 and #3 where evaluated only in the Sound and Voidconditions, with results of comparable pattern and magnitude to thosedocumented for #1A and #1B. Overall, the impedance measurements wereconsistent with anticipated behavior and supported the use of thatvariable as a useful indicator of grout condition for the imagingapplication intended.

The cross-sectional image display generated by the TIU 100 isexemplified by the patterns in FIG. 5. Please note that dashed anddotted lines were added for reference to show where voids and individualstrands were present in the specimens. In the figure, the outer blackring in the images was scaled to correspond to the actual dimensions ofthe polymer duct 150. At each rotation angle, the radius line from thecenter to the inner part of the polymer duct 150 was divided into twosegments. The inner region, colored green extended from the center ofthe duct 150 to the steel strand envelope, which was located at eachangle at the radius value determined by the magnetic sensing techniquedescribed previously. The outer segment extended from the strandenvelope radius until the inner surface of the duct 150. That segmentwas colored white for an impedance value at that angle indicative of afully sound grout condition (S), solid red for a full void indication(V), or solid blue for indication of a highly conductive medium such asbleed water. Intermediate impedance values that would be obtainedbetween full void or fully sound grout indications, such as the case apartial void or the transition between a void and sound grout, receiveda correspondingly intermediate shade between red and white. Conversely,intermediate conditions where impedance decreased with respect to thatof sound grout, for example highly dilute water (DW), or grout with ahigh water/grout ratio (CW), received a corresponding shade between blueand white. Graphically joining the radial segments into a polar diagramcreated the displayed image of the cross section with visual flagging ofgrout deficiencies and their character and extent.

For appropriate mapping with reasonable noise rejection and simplicityof interpretation, a calibration and proportioning procedure wasestablished, aimed to field operation. Calibration is ideally performedwhen having access to a portion of the tendon 140 to be assessed, or ofa tendon representative of a population of similarly constructed peertendons, having a reasonable expectation of containing grout absent ofdeficiencies. In that case, the TIU 100 is placed on the tendon 140 andan angular impedance profile is obtained. That profile is anticipated toshow only modest variation, exemplified by the data for the Soundcondition in FIG. 4. For simplicity that variation is ignored and theaverage value of |Z| over the 360° interval is computed and used as theimpedance value descriptive of the sound ground condition. Proportionaldeviations from that value above and below representative of void andwater conditions respectively are then assigned based on the variationsobserved in the laboratory specimens, and then used to assign colors.The assignment limits can be readily changed in the processing softwarevia a suitable graphical user interface.

The result of the above tests and processing was a highly-descriptivevisualization of the inside cross section of the tendon 140 withidentification of grouting anomalies. The top part of FIG. 5 displaysthe results obtained with Specimen #1B, clearly differentiating theconditions discussed in the previous section, and in the context of theposition relative to the strand presence in the cross section. It shouldbe recalled that, as stated earlier, differentiation was less precisefor grouting issues that resulted in lowered impedance relative to thatof sound grout. Similar graphs for Specimen #1B adequately flagged thepresence of water but showed similarly strong color intensity for boththe dilute and the conductive variations. The lower part of FIG. 5 showsthe results for the larger diameter tendon samples #2 and #3. There theposition and presence of a full void was also successfully identified inboth cases, even in the case of the actual bridge tendon (#3) when thevoid was associated with a relatively small grout space thickness.Alternative display modes of the same information can be used as well.The outer radial segment was divided into two parts, with the inner partwhite. For a void indication, the part closest to the duct wall wascolored solid red and occupied a fraction of the outer radial segmentlength proportional to how much a full void condition was approached.For an elevated grout conduction condition, a complementary solid bluescheme applied. The result was a faux designation of anomaly position(always close to the duct wall) but with a bold color pattern for easierflagging of marginal cases.

It is noted that the TIU 100 consistently recovered the general shapeand dimensions of the strand bundle envelope, as can be seen bycomparison with the actual strand placement. Some deviations fromprecise recovery existed, mainly in the laboratory specimens, wherebythe size of the bundle was modestly overestimated at angular positionsfurther removed from the duct wall. This deviation has been ascribed tothe relatively high magnetic permeability of the grout used to preparethe tendon samples, which resulted in a minor increase in the magneticforce on the sensing magnet 115 with consequent underestimation of thestrand-magnet distance. Similar effects have been noted in rebarlocation sensors when working with certain cementitious materials andcorrective formulas to minimize this source of strand positionuncertainty were developed. These corrections can be approximated by aminor flat amount subtraction from the magnetic force measured as usedin Equation 2 and were implemented in TIU processing software, invarious embodiments.

Based on comparative analysis, an exemplary tendon imaging unit 100detects full and outer voids within sample tendons providing comparableresults to those of Gamma Ray Tomography but with minimum operatorrequirements, minimum equipment cost, and minimal health risks. Forfield demonstration, a prototype TIU 100 was deployed to the JohnRingling Causeway Bridge in Sarasota, Fla. and tested on two externalfield tendons. Prior repairs had replaced other tendons in the bridgethat had clear signs of distress, so based on that and based on previoustesting, the remaining tendons were deemed not likely to have severegrout deficiencies. Consistent with that expectation, the TIU 100identified only normal grout there. The tests nevertheless demonstratedthe ability of the TIU 100 to obtain reliable and repeatablecross-sectional images of the tested tendons, with clear differentiationof strand envelope patterns. Ease of operation by non-specialistpersonnel with minimal training, and ability to provide nearlyinstantaneous images in a field setting by a robust unit with nobreakdowns, were demonstrated as well. Such an approach represents adesirable balance between sophistication and equipment/operation costs.Thus, in practical circumstances, systems and methods of the presentdisclosure can make timely assessment of a large inventory of tendons ina bridge possible, where application of other technologies could havebeen prohibitively expensive and slow, or limited to only a smallselection of tendons.

In accordance with the present disclosure, various systems and methodsfor imaging grout deficiencies in external tendons have been presented.In various embodiments, magnetic measurements are used to image thestrand bundle and impedance measurements are used to identify groutdeficiencies in the space between the strand bundle and the tendon duct150. In an exemplary system or apparatus, magnetic and impedance sensorsare physically integrated in a tendon imaging unit 100 (via impedancesensor assembly 120) that is suitable for field measurements in actualbridge tendons 140. From magnetic and impedance measurements, anexemplary TIU system can recover a strand bundle envelope andindications of grout conditions in a non-intrusive manner. As such, inan exemplary embodiment, the TIU 100 can produce a color-coded image ofthe tendon cross section rapidly displaying the position of the strandbundle, detecting voids, and displaying a condition of the grout 170within the tendon enclosure based on a combination of the impedance datawith the strand position information (obtained from magnetic attractionforce measurements). These types of images of the cross section ofexternal post tensioned tendons used in highway bridges can revealgrouting deficiencies that could possibly cause corrosion of the tendonsteel strands and may lead to eventual failure of those criticalcomponents, if not corrected. It is important to detect deficienciesduring inspection of existing bridges, and if possible during theconstruction phase to enable early remedial measures.

It should be emphasized that the above-described embodiments of thepresent disclosure are merely possible examples of implementations,merely set forth for a clear understanding of the principles of thedisclosure. Many variations and modifications may be made to theabove-described embodiment(s) without departing substantially from theprinciples of the disclosure. All such modifications and variations areintended to be included herein within the scope of this disclosure andprotected by the following claims.

The invention claimed is:
 1. A system for indicating a grout conditionwithin a post-tensioned tendon, the system comprising: a force measuringsensor that provides data indicating magnetic forces applied to amagnet; an impedance sensor that provides measurement data involving animpedance between a metallic sensing plate and metallic strands withinthe post-tensioned tendon; a mechanism adapted to mount to thepost-tensioned tendon and position the magnet and the metallic sensingplate in close proximity to an outer surface of the tendon, themechanism further being adapted to facilitate moving of the magnet andthe metallic sensing plate around the outer surface of thepost-tensioned tendon; and a computing device that is configured togenerate an image of a cross-section of the post-tensioned tendonindicating one or more grout conditions in spatial proximity to themetallic strands within the post-tensioned tendon based on at least dataprovided by the impedance sensor and the force measuring sensor.
 2. Thesystem of claim 1, wherein grout conditions are identified by a colormapping based on the data provided by the impedance sensor.
 3. Thesystem of claim 2, wherein a first color represents a normal groutcondition, a second color represents a full void grout condition, and athird color represents a partial void grout condition.
 4. The system ofclaim 3, wherein a shading of the third color represents a concentrationlevel of water that is partially filling a void in grout material. 5.The system of claim 1, further comprising an angular positioning modulethat tracks positioning of the magnet and the metallic sensing plate aseach travels around the outer surface of the post-tensioned tendon. 6.The system of claim 1, wherein the force measuring sensor is a loadcell.
 7. The system of claim 1, wherein the mechanism includes a shellmember that mounts to the tendon.
 8. The system of claim 7, wherein themagnet and the metallic sensing plate are accommodated at oppositepoints of a circumference of the shell member.
 9. The system of claim 1,wherein the computing device is configured to determine positioning ofthe metallic strands based upon force data supplied by the forcemeasuring sensor.
 10. The system of claim 9, wherein the computingdevice is configured to generate a radial plot of the tendon thatidentifies strand positions.
 11. A method of indicating a groutcondition within a post-tensioned tendon, the method comprising:positioning a magnet and a metallic sensing plate in close proximity toan outer surface of the post-tensioned tendon; rotating the magnet andthe metallic sensing plate around the outer surface of thepost-tensioned tendon; measuring an amount of magnetic forces applied tothe magnet during rotation of the magnet around the post-tensionedtendon; measuring an impedance between the metallic sensing plate andmetallic strands within the post-tensioned tendon during rotation of themetallic sensing plate around the post-tensioned tendon; and generatingan image of a cross-section of the post-tensioned tendon indicating oneor more grout conditions in spatial proximity to the metallic strandswithin the post-tensioned tendon based on measurement data using themagnet and the metallic sensing plate.
 12. The method of claim 11,wherein the image is generated by deconvoluting magnetic force values togenerate a radial plot that provides an indication of a location of thestrands within the tendon.
 13. The method of claim 12, wherein the imageis generated by assigning a color-code to impedance measurement dataobtained from the metallic sensing plate.
 14. The method of claim 13,wherein a first color represents a normal grout condition, a secondcolor represents a full void grout condition, and a third colorrepresents a partial void grout condition.
 15. The method of claim 14,wherein a shading of the third color represents a concentration level ofwater that is partially filling the void in grout material.
 16. Themethod of claim 11, further comprising tracking positioning of themagnet and the metallic sensing plate as each travels around the outersurface of the post-tensioned tendon.
 17. The method of claim 11,further comprising mounting the magnet and the metallic sensing plate tothe outer surface of the post-tensioned tendon.
 18. The method of claim17, wherein the magnet and the metallic sensing plate are integratedwithin a shell member that mounts to the post-tensioned tendon.
 19. Themethod of claim 18, wherein the magnet and the metallic sensing plateare accommodated at opposite points of a circumference of the shellmember.
 20. The method of claim 11, further comprising determiningpositioning of the strands based upon force data involving the magnet.